Critical limit one-point correlations of monodromy fields on 321-1321-1321-1

Monodromy fields on ?² are a family of lattice fields in two dimensions which are a natural generalization of the two dimensional Ising field occurring in theC ^*-algebra approach to Statistical Mechanics. A criterion for the critical limit one point correlation of the monodromy field σ_a(M) at a ∈ ?², $$mathop {lim }limits_{s uparrow 1} leftlangle {sigma _a (M)} rightrangle ,$$ is deduced for matrices M ∈ GL(p,?) having non-negative eigenvalues. Using this criterion non-identity 2×2 matrices are found with finite critical limit one point correlation. The general set ofp×p matrices with finite critical limit one point correlations is also considered and a conjecture for the critical limitn point correlations postulated.